Conventionally, there have been known a grid method and a particle method as a method for analyzing a behavior of a fluid or the like. Among them, the grid method is a method for determining a velocity, a pressure and other characteristics of the fluid or the like in each of grid positions by covering a region to be analyzed by a grid, and various methods such as a difference method, a finite element method, and a finite volume method exist. In the grid method, however, it is hard to deal with a large deformation such as a splash of a free surface (interface), and the grid method includes such a defect that a complicated work to prepare a grid in the subject domain is necessary.
On the contrary, the particle method expresses the fluid or the like as an assembly of particles, and analyzes a behavior of the fluid or the like by calculating a mutual action between the particles. Accordingly, the particle method does not require a grid generation which is carried out in the grid method, and has an advantage of handling large deformations of the free surface comparatively easily.
In this case, as the particle methods, there have been known an SPH method for calculating a behavior of a compressible fluid in accordance with an explicit scheme and a MPS method for calculating a behavior of an incompressible fluid in accordance with a semi-implicit scheme. A technique related to the latter is known by the following PTL 1 and PTL 2. Further, there has been known an ISPH method which can analyze the incompressible fluid by introducing an algorithm of the semi-implicit scheme to the SPH method, without introducing an artificial viscosity.
In the case of analyzing the behavior of an incompressible fluid by using the particle method, particularly the MPS method, a particle number density in a predetermined reference radius (within a reference range) based on one particle in the fluid takes a fixed value, under an incompressible condition. Accordingly, in the MPS method, the behavior of the fluid is analyzed by correcting a velocity and a position of the particle in such a manner that the particle number density always takes a constant value.
Further, in the MPS method, in order to determine whether or not a particle is positioned on an upper surface (a free surface; an interface) of a fluid, it is determined whether or not a particle number density ni at a position of the particle satisfies a condition of the following equation (1) with respect to a fixed value n0.ni<βn0  (1)
(where, β is a model constant (recommended value β=0.97))
On the other hand, in the SPH method, in the case that density ρi of a fluid, in place of the particle number density ni, satisfies a condition of the following equation (2) with respect to a fixed value ρ0, it is determined that the particle is a particle which is positioned on the free surface.ρi<βρ0  (2)
(where, β is a model constant (recommended value β=0.99))
In the case of the incompressible fluid, since the particle number density in the reference range is in proportion to the density of the fluid, approximately the same determination is carried out by Equation (1) and Equation (2).
However, there are cases that a particle which is not a particle positioned on the free surface (i.e., a particle inside the fluid) is also determined to be the free surface particle, if the determination mentioned above only is carried out. FIG. 7 shows a result obtained by analyzing the fluid in a tank in accordance with the MPS method, the particle determined to be the particle on the free surface in accordance with the method mentioned above is indicated by ●, and the particle determined not to be a free-surface particle is indicated by ◯. As it is apparent from this result, in the conventional interface determining method, there have been erroneous determinations that the free surface particle appears inside of the fluid.